Calculus
A function f(x)f\(\left\)(x\(\right\)) has the following properties:
f′(x)>0f^{\(\prime\)}\(\left\)(x\(\right\))>0 and f′f^{\(\prime\)}′(x)>0^{\(\prime\)}\(\left\)(x\(\right\))>0, for x>4x>4
Which of the following is a possible graph of f(x)f\(\left\)(x\(\right\))?
Graph the function f(x)=6−6x23+x83f\(\left\)(x\(\right\))=6-6x^{\(\frac\)23}+x^{\(\frac\)83}. The first and second derivative are given.
f′(x)=−4x13+83x53f^{\(\prime\)}\(\left\)(x\(\right\))=-\(\frac{4}{x^{\frac13}\)}+\(\frac\)83x^{\(\frac\)53}
f′′(x)=43x43+409x23f^{\(\prime\)\(\prime\)}\(\left\)(x\(\right\))=\(\frac{4}{3x^{\frac43}\)}+\(\frac{40}{9}\)x^{\(\frac\)23}
Graph the given classical curve using analytical methods.
y2=x3−2x+3y^2=x^3-2x+3 ; dydx=3x2−22y\(\frac{dy}{dx}\)=\(\frac{3x^2-2}{2y}\)
